A hybrid technique for the solution of unsteady Maxwell fluid with fractional derivatives due to tangential shear stress
- Authors: Raza N.1, Shahid I.1, Abdullah M.1
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Affiliations:
- Department of Mathematics
- Issue: Vol 52, No 6 (2017)
- Pages: 713-721
- Section: Article
- URL: https://journals.rcsi.science/0015-4628/article/view/155695
- DOI: https://doi.org/10.1134/S0015462817060027
- ID: 155695
Cite item
Abstract
The article describes the unsteady motion of viscoelastic fluid for a Maxwell model with fractional derivatives. The flow is produced by cylinder, considering time dependent quadratic shear stress ft2 on Maxwell fluid with fractional derivatives. The fractional calculus approach is used in the constitutive relationship of Maxwell model. By applying Laplace transform with respect to time t and modified Bessel functions, semianalytical solutions for velocity function and tangential shear stress are obtained. The obtained semianalytical results are presented in transform domain, satisfy both initial and boundary conditions. Our solutions particularized to Newtonian and Maxwell fluids having typical derivatives. The inverse Laplace transform has been calculated numerically. The numerical results for velocity function are shown in Table by using MATLAB program and compared them with two other algorithms in order to provide validation of obtained results. The influence of fractional parameters and material constants on the velocity field and tangential stress is analyzed by graphs.
About the authors
Nauman Raza
Department of Mathematics
Author for correspondence.
Email: abdul4909@gmail.com
Pakistan, Lahore, 54590
Iqra Shahid
Department of Mathematics
Email: abdul4909@gmail.com
Pakistan, Lahore, 54590
M. Abdullah
Department of Mathematics
Email: abdul4909@gmail.com
Pakistan, Lahore, 54890
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